Numerical schemes for the optimal input flow of a supply-chain
Abstract
An innovative numerical technique is presented to adjust the inflow to a supply chain in order to achieve a desired outflow, reducing the costs of inventory, or the goods timing in warehouses. The supply chain is modelled by a conservation law for the density of processed parts coupled to an ODE for the queue buffer occupancy. The control problem is stated as the minimization of a cost functional J measuring the queue size and the quadratic difference between the outflow and the expected one. The main novelty is the extensive use of generalized tangent vectors to a piecewise constant control, which represent time shifts of discontinuity points. Such method allows convergence results and error estimates for an Upwind- Euler steepest descent algorithm, which is also tested by numerical simulations.
Keywords
Cite
@article{arxiv.1208.4824,
title = {Numerical schemes for the optimal input flow of a supply-chain},
author = {Ciro D'Apice and Rosanna Manzo and Benedetto Piccoli},
journal= {arXiv preprint arXiv:1208.4824},
year = {2015}
}